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The Celtics are close to resolving their most pressing offseason issue as talks with Paul Pierce on a long-term contract extension have progressed extensively, according to sources with firsthand knowledge of the negotiations.

Despite several reports that a deal has been consummated, there has been no agreement on a potential four-year contract, according to the source, and there was little progress made yesterday.

The Pierce camp would like a four-year, fully guaranteed deal at about $15 million per season, but the Celtics are haggling as to whether to fully guarantee the fourth year, which would end the contract when Pierce is 36.

The sides have been talking since Pierce opted out of the final year of his contract, worth $21.5 million, late Tuesday night. Pierce, according to those close to the situation, has not negotiated with another club. The sides can only agree on a deal at this point; free agent contracts cannot be officially signed until July 8.

Pierce is not only accepting a reduction from the $19.7 million salary he earned last season but he will likely accept more than $5 million less per season than he could have earned with a maximum contract.

Pierce was eligible for the highest scale maximum deal because of his 12 years of NBA experience, meaning the Celtics could have paid him at least $20.7 million for the first season and $28.9 million in the final season.

Instead, Pierce is taking long-term security and the opportunity to finish his career in Boston.

Celtics president Danny Ainge said this week the team’s first priority was to re-sign Pierce and that effort was aided by the return of coach Doc Rivers, who announced the day after Pierce opted out that he would coach again next season.

Pierce encouraged Rivers several times to remain coach and said the team enjoyed playing under his instruction. So Rivers’s decision could not only foster the re-signing of Pierce but also Ray Allen, who has not been linked to any other team since becoming a free agent Thursday.

Rivers said the Celtics brass needed to work arduously on re-recruiting Pierce and Allen, especially considering the number of teams with money to spend. Players such as Joe Johnson (expected to sign a maximum deal with the Hawks) and Rudy Gay (a max deal with the Grizzlies) are off the market, while the free agent Big Three — LeBron James, Dwyane Wade, and Chris Bosh — have yet to decide.

No matter where they decide to sign, there will be several teams (Nets and Clippers?) without a major star and yet with enough cap space for a lucrative contract.

Meanwhile, the team’s search for a big man has spread to Dallas center Brendan Haywood, but bringing him to Boston would require a sign-and-trade because the Celtics likely could not afford Haywood’s asking price.

Boston is seeking a starting center until the return of Kendrick Perkins from ACL surgery in early 2011. Haywood has intimated he wants to start next season, regardless of where he signs.

The Celtics are expected to reach out to more moderately priced centers and also have Rasheed Wallace’s contract to dangle in a trade.

Because Wallace has not officially retired, the Celtics can trade him to another club, who could gain salary-cap relief if he officially retires this summer. So Wallace could leave Boston giving the Celtics one final lift off the bench.